Combinatorics and Probability

Abstract

We conclude the book with combinatorics. First, we train combinatorial skills in set theory and geometry, with a glimpse at permutations. Then we turn to some specific techniques: generating functions, counting arguments, the inclusion-exclusion principle. A strong accent is placed on binomial coefficients.

This is followed by probability, which, in fact, should be treated separately. But the level of this book restricts us to problems that use counting, classical schemes such as the Bernoulli and Poisson schemes and Bayes’ theorem, recurrences, and some minor geometric considerations. It is only later in the development of mathematics that probability loses its combinatorial flavor and borrows the analytical tools of Lebesgue integration.